haese225 Posted September 5, 2016 Report Share Posted September 5, 2016 (edited) If Z~N(0,1), prove that for positive k: P(|Z|<k) = 2 - 2Φ(k). I'm pretty certain the 2 - 2Φ(k) part comes from symmetry with the distribution if Φ(k) is negative. Pretty tough question but here's my working. Hoping someone can develop this further... Thanks Edited September 5, 2016 by 4lan Reply Link to post Share on other sites More sharing options...
kw0573 Posted September 5, 2016 Report Share Posted September 5, 2016 The phi of x is the probabilitiy density function, for which its area under the curve are the probabilities. So basically question asks to prove a relationahip between the cumulative density and the probability density functions, that of which applies to -k to k of the standard normal distribution. However the relationship is not true, because for large k, say k = 1000, phi pf k is very close to 0, and 2-2* 0.00 is 2, which is not a valid probability. Also not sure why you sketch a bimodal distribution, when you are dealing with normal distribution. Reply Link to post Share on other sites More sharing options...
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